A calendar was any system of measuring long periods of time, including days, months, and years. In Human culture, the term also referred to a series of visual charts, usually representing months, used to keep track of such calendar.
In the ancient past, a being known as Kukulkan gave the Mayan civilization on Earth a remarkably accurate calendar, according to which the Mayans were supposed to build a city awaiting his return. (TAS: "How Sharper Than a Serpent's Tooth")
A digital calendar was present on the wall of Sanctuary District A's processing center in 2024. After Commander Benjamin Sisko and Doctor Julian Bashir were inadvertently sent back in time due to a transporter accident in 2371, Sisko noted the date on the wall calendar to be August thirteenth, a few days prior to the Bell Riots. (DS9: "Past Tense, Part I")
In 2376, Neelix proposed a riddle to Tuvok while the two were on an away mission: an ensign was stranded on an uninhabited moon, without food, and all he had was a calendar. How could he survive? Eventually, Tuvok came to the "illogical" conclusion that the ensign could survive by eating the "Sundays," though the original answer was that he had "feasted on the dates." (VOY: "Riddles")